Internal State Variable Approach for Predicting Stiffness Reductions in Fibrous Laminated Composites with Matrix Cracks

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Abstract
A mathematical model utilizing the Internal State Variable (ISV) concept is proposed for predicting the upper bound of the reduced axial stiffnesses in cross-ply lami nates with matrix cracks. The axial crack opening displacement is explicitly expressed in terms of the observable axial strain and the undamaged material properties. A crack parameter representing the effect of matrix cracks on the observable axial Young's modulus is calculated for glass/epoxy and graphite/epoxy material systems. The results of the present study show that the matrix crack opening displacement and conse quently the effective Young's modulus depends not on the crack length but on its ratio to the crack spacing. Comparisons of the present model with experimental data and other models in the litera ture show a good agreement, thus confirming direct applicability of the model to [0 p/90 r] s type laminates.